You don't have to like David Bowie, it doesn't bother me, but I do both as a singer and an actor. One of favourite films is Labyrinth, I can watch it again and again.
At one point the characters have to cross a bridge but it's guarded by a knight who will fight anyone who tries to cross it "without my permission!". After being beaten to a standstill by the knight the main character finally just asks for permission. The knight is a bit surprised by this turn of events - apparently nobody ever just asks - gives it.
This is the whole point when it comes to production companies who don't accept "unsolicited" scripts, because everybody really really wants to find good writers and hopefully good scripts.
It's the query letter or email.
I have quite a high success rate getting my scripts read by industry peeps because I get them to solicit my scripts even without representation.
My feeling is that an old-fashioned snail-mail query letter is easy to ignore and forget - what you need is a good brief email. Since I'm more of a TV writer (I'll get the hang of features one day) I tend to target TV companies. I find ones that produce things I like and are the sort of things I write. I check their website for the the right person to contact, find the email address and write a concise (sometimes not so concise) email explaining who I am, my writing credentials (such as they are) and ask them whether they'd be interested in reading my work.
Humility is called for - and a good choice of subject line. I have a subject line that works really well in all circumstances, and I'm not saying what it is (sorry).
I've even used this approach successfully with the BBC.
I personally think the key is to realise that you're selling yourself as a writer rather than attempting to push a particular script. Almost all writing jobs in film and TV will be writing what someone else wants, it's very rare to get a spec made until you've made a name for yourself, sometimes not even then.
If your scripts, or parts of them, are available on the web so much the better - then you can just direct people to the correct URL. It makes it really easy for them and that's important, the fewer barriers between them and your script, the better. It's also useful if you have more than one - just to prove you're not a one-script wonder.
I mention all this because I got an email yesterday from a production company as a response to one of these query emails. And they will be reading my scripts (plural).
Nothing may come of it, but at the very least (for better or worse) they now know my name.
What's on the turntable? "Mobocaster" by Tangerine Dream from "Tang-Go"